Short answer: No.
I went in both stores and compared the same product and it turns out that Bulk Barn is not cheaper than grocery stores.
Source
So if I calculate for the price per 1g:
Bulk Barn = .027$ per 1g
Food Basics (using regular price: $4.99) = .023$ per 1g
Food Basics is cheaper and they even have discounts which makes the spread bigger.
Details
Stores: Food Basics v Bulk Barn
Day: Same day
Item: Reese’s mini cups
Time: Jun 2024